The generator matrix

 1  0  0  0  0  1  1  1 X^2  1 X^2+X  1
 0  1  0  0  0 X^2 X^2 X+1  X X^2+1  1  X
 0  0  1  0  0 X^2+X  1 X^2+1  1 X+1 X^2+X  X
 0  0  0  1  0 X+1  1 X^2+X X^2+1  1  0 X^2
 0  0  0  0  1  1  X X+1 X^2+1 X^2+X X+1  0

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+154x^7+569x^8+1608x^9+3870x^10+6156x^11+7998x^12+6216x^13+3921x^14+1578x^15+520x^16+160x^17+16x^18+1x^22

The gray image is a linear code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.13 in 0.719 seconds.